Download e-book for iPad: Algebraic Geometry Proc. conf. Chicago, 1989 by Spencer Bloch, Igor V. Dolgachev, William Fulton

By Spencer Bloch, Igor V. Dolgachev, William Fulton

ISBN-10: 0387544569

ISBN-13: 9780387544564

ISBN-10: 3540544569

ISBN-13: 9783540544562

This quantity comprises the complaints of a joint USA-USSR symposium on algebraic geometry, held in Chicago, united states, in June-July 1989.

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Another simple Cl -clasper G) (see Figure 4). Then LT is Ck+1 -equivalent to LT , LT is Ck+1 -equivalent to LT , and LT ∪G is Ck+l+1 -equivalent to LT ∪G . T Ki T' Ki T T T'' T'' T G T''' G Fig. 4. 1. It is wellknown that a2 is an order-2 Vassiliev invariant, and C3 -equivalence preserves the order-2 Vassiliev invariants. So f (L) is a C3 -equivalence invarinat. Let L be a 2-string link that obtained from L by a single self C2 -move. We may assume that there is a simple C2 -clasper T such that L∩T = K1 ∩T and L is obtained from L by surgery along T .

Invariance under Reidemeister moves In this section we shall deal with the natural question of whether the equivariant Khovanov homology defined in section 3, is an invariant of periodic links. In other words, we would like to discuss whether this construction is invariant under Reidemeister moves. Let D and D be two p−periodic diagrams which represent the same link L. Obviously, D and D are related by Reidemeister moves. Since D and D are both p−periodic, then the Reidemeister moves which relate D and D are applied along orbits of the action defined by the rotation ϕ.

This completes the proof of this lemma. 3. The Morse-Novikov numbers for prime knots of ≤ 10 crossings and links of ≤ 9 crossings In this section, we assume that a knot or link is prime. The fibred knots up to 10 crossings and fibred links up to 9 crossings have been detected by Kanenobu ([7]) and Gabai ([1]). Note that there exist 2n−1 orientation classes to analyze for a given link of n components. By using Heegaard splitting associated to the Morse map, we can show that MN (L) = 2 if L is a non-fibred knot up to 10 crossings or link up to 9 crossings.

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Algebraic Geometry Proc. conf. Chicago, 1989 by Spencer Bloch, Igor V. Dolgachev, William Fulton

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